Question

Which of the following is the product of the rational expression shown below

Answer 1

Option C: $\frac{x^{2}-9}{x^{2}-4}$ is the product of the rational expression.

Explanation:

The given rational expression is $\frac{x+3}{x+2} \cdot \frac{x-3}{x-2}$

We need to determine the product of the rational expression.

Product of the rational expression:

Let us multiply the rational expression to determine the product of the rational expression.

Thus, we have;

$\frac{(x+3)(x-3)}{(x+2)(x-2)}$

Let us use the identity $(a+b)(a-b)=a^2-b^2$ in the above expression.

Thus, we get;

$\frac{x^{2} -3^2}{x^{2} -2^2}$

Simplifying the terms, we get;

$\frac{x^{2}-9}{x^{2}-4}$

Thus, the product of the rational expression is $\frac{x^{2}-9}{x^{2}-4}$

Hence, Option C is the correct answer.